Generally speaking allergies are your body's reaction to substances, foods, particles, insect bites, etc. If you've never been exposed to a certain allergen, you'll probably not react to it the first time. Your body's immune system may look at the allergen and shrug it off... or it might recognise the exposure as a threat and post a heavy guard and release excess antigens or antibodies on the NEXT exposure.

This explains why those with food or pet (cats, dogs, horses) allergies will have the same issues on the island. People will be less likely to bring their hay fever symptoms with them to the island, unless there are similar plants where they live.

Mrs. dirtleg has terrible hay fever and allergies. We live in hay fever central in St. Louis. But in Jamaica she has had very little problem with them, she even sleeps well at CSA, which surprised her on our first trip. The only time she had a problem was when she got too close to the flowers in the lobby on arrival. She wanted to see if they were real. They were, and she sniffled and sneezed for a half hour.